On Pólya groups of some non-Galois number fields
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916361036365824 |
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| author | Maarefparvar, Abbas |
| author_facet | Maarefparvar, Abbas |
| contents | We prove two conjectures proposed by Chabert and Halberstadt concerning Pólya groups of $S_4$-fields and $D_4$-fields. More generally, the latter will be proved for $D_n$-fields with $n \geq 4$ an even integer. Further, generalizing a result of Zantema, we also prove that the pre-Pólya group of a non-Galois field of a prime degree, e.g. an $A_5$-field, coincides with its Pólya group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09019 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Pólya groups of some non-Galois number fields Maarefparvar, Abbas Number Theory 11R21, 11R29, 11R37 We prove two conjectures proposed by Chabert and Halberstadt concerning Pólya groups of $S_4$-fields and $D_4$-fields. More generally, the latter will be proved for $D_n$-fields with $n \geq 4$ an even integer. Further, generalizing a result of Zantema, we also prove that the pre-Pólya group of a non-Galois field of a prime degree, e.g. an $A_5$-field, coincides with its Pólya group. |
| title | On Pólya groups of some non-Galois number fields |
| topic | Number Theory 11R21, 11R29, 11R37 |
| url | https://arxiv.org/abs/2408.09019 |